7-5 Box-and-Whisker Plots

Course 2

Warm UpUse the data below for Questions 1-4.14, 25, 37, 53, 26, 12, 70, 31

1. What is the mean?2. What is the median?3. What is the mode?4. What is the range?

33.528.5

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Course 2

7-5 Box-and-Whisker Plots

Learn to display and analyze data inbox-and-whisker plots.

Course 2

7-5 Box-and-Whisker Plots

Course 2

7-5 Box-and-Whisker Plots

A box-and-whisker plot uses a number line to show the distribution of a set of data.

• First, put the data in order from smallest to largest.

• Then find the median.

Course 2

7-5 Box-and-Whisker Plots

The lower quartile is the median of the data between the smallest number and the median of the entire data set.

67 67 69 73 75 75 81 85

Lower quartile

• After you find the median, the data is split in half.

• Now find the median of the “lower” half of the data, meaning from the smallest number to the original median.

Course 2

7-5 Box-and-Whisker Plots

The upper quartile is the median of the data between the median of the entire data set and the largest number.

67 67 69 73 75 75 81 85

Upperquartile

• After you find the median, the data is split in half.

• Now find the median of the “upper” half of the data, meaning from the original median to the largest number.

Course 2

7-5 Box-and-Whisker Plots

The interquartile range is the difference between the upper and the lower quartiles.

• The interquartile range is represented by the box in a box-and-whisker plot.

• The longer the box, the greater the interquartile range.

Interquartile range

Course 2

7-5 Box-and-Whisker Plots

To find the median of a data set with an even number of values, find the mean of the two middle values.

Caution!

Use the data to make a box-and-whisker plot.

Additional Example 1: Making a Box-and-Whisker Plot

Course 2

7-5 Box-and-Whisker Plots

73 67 75 81 67 75 85 69

Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upper quartiles.

The least value. The greatest value.

67 67 69 73 75 75 81 85

Find the median.67 67 69 73 75 75 81 852+

=74

Additional Example 1 Continued

Course 2

7-5 Box-and-Whisker Plots

67 67 69 73 75 75 81 85

lower quartile = 67 + 692

= 68

upper quartile = 75 + 812 = 78

Step 1 Continued

Additional Example 1 Continued

Course 2

7-5 Box-and-Whisker Plots

Step 2: Draw a number line.

64 66 68 70 72 74 76 78 80 82 84 86

Above the number line, plot points for each value in Step 1.

Step 3: Draw a box from the lower to the upper quartile. Inside the box, draw a vertical line through the median.Then draw the “whiskers” from the box to the least and greatest values.

Check It Out: Example 1

Course 2

7-5 Box-and-Whisker Plots

Use the data to make a box-and-whisker plot.

42 22 31 27 24 38 35

22 24 27 31 35 38 42

22 24 27 31 35 38 42

The least value.The greatest value.

The median.

The upper and lower quartiles.22 24 27 31 35 38 42

Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upper quartiles.

Check It Out: Example 1 Continued

Course 2

7-5 Box-and-Whisker Plots

Step 2: Draw a number line.

20 22 24 26 28 30 32 34 36 38 40 42

Above the number line, plot a point for each value in Step 1.

Step 3: Draw a box from the lower to the upper quartile. Inside the box, draw a vertical line through the median.Then draw the “whiskers” from the box to the least and greatest values.

Use the box-and-whisker plots below to answer each question.

Additional Example 2A: Comparing Box-and-Whisker Plot

Course 2

7-5 Box-and-Whisker Plots

Which set of heights of players has a greater median?The median height of basketball players, about 74 inches, is greater than the median height of baseball players, about 70 inches.

64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.)

Basketball Players

Baseball Players

Use the box-and-whisker plots below to answer each question.

Additional Example 2B: Comparing Box-and-Whisker Plot

Course 2

7-5 Box-and-Whisker Plots

Which players have a greater interquartile range?

The basketball players have a longer box, so they have a greater interquartile range.

64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.)

Basketball Players

Baseball Players

Use the box-and-whisker plots below to answer each question.

Additional Example 2C: Comparing Box-and-Whisker Plot

Course 2

7-5 Box-and-Whisker Plots

Which group of players has more predictability in their height?The range and interquartile range are smaller for the baseball players, so the heights for the baseball players are more predictable.

64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.)

Basketball Players

Baseball Players

Use the box-and-whisker plots below to answer each question.

Check It Out: Example 2A

Course 2

7-5 Box-and-Whisker Plots

Which shoe store has a greater median?The median number of shoes sold in one week at Sage’s Shoe Store, about 32, is greater than the median number of shoes sold in one week at Maroon’s Shoe Store, about 28.

20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store

Maroon’s Shoe Store

Sage’s Shoe Store

Use the box-and-whisker plots below to answer each question.

Check It Out: Example 2B

Course 2

7-5 Box-and-Whisker Plots

Which shoe store has a greater interquartile range?Maroon’s shoe store has a longer box, so it has a greater interquartile range.

20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store

Maroon’s Shoe Store

Sage’s Shoe Store

Use the box-and-whisker plots below to answer each question.

Check It Out: Example 2C

Course 2

7-5 Box-and-Whisker Plots

Which shoe store appears to be more predictable in the number of shoes sold per week?The range and interquartile range are smaller for Sage’s Shoe Store, so the number of shoes sold per week is more predictable at. Sage’s Shoe Store.

20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store

Maroon’s Shoe Store

Sage’s Shoe Store

Lesson Quiz: Part IUse the data for Questions 1-3.24, 20, 18, 25, 22, 32, 30, 29, 35, 30, 28, 24, 381. Create a box-and-whisker plot for the data.2. What is the range?3. What is the 3rd quartile?

20

31

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7-5 Box-and-Whisker Plots

18 20 22 24 26 28 30 32 34 36 38 40

Lesson Quiz: Part II

4. Compare the box-and-whisker plots below. Which has the greater interquartile range?

They are the same.

Course 2

7-5 Box-and-Whisker Plots

18 20 22 24 26 28 30 32 34 36 38 40